Details

Time bar (total: 8.2s)

analyze1.8s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14

sample104.0ms

Algorithm
intervals
Results
36.0ms37×body1280valid
26.0ms46×body640valid
16.0ms136×body80valid
7.0ms18×body320valid
5.0ms19×body160valid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0550124

prune14.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.7b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.1b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
8.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
18.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
33.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
40.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
45.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify88.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
049831601
149831601

prune256.0ms

Filtered
67 candidates to 97 candidates (-44.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New88997
Fresh101
Picked011
Done000
Total891099

Merged error: 10.8b

Counts
99 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

2.4b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.6b
(* J (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))))
12.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.4b
(cbrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×cbrt-prod
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cube-cbrt add-cbrt-cube
7×sqrt-prod
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 associate-*l* pow-prod-down prod-exp cbrt-unprod flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*r* *-commutative
Counts
4 → 67
Calls
4 calls:
9.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
5.0ms
(* J (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))))
7.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.0ms
(cbrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
31.0ms
(* J (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))))
64.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
66.0ms
(cbrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

simplify69.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049091649
149091649

prune346.0ms

Filtered
62 candidates to 79 candidates (-27.4%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New76379
Fresh178
Picked101
Done011
Total781189

Merged error: 10.8b

Counts
89 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
7.1b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.6b
(* (* (* -2.0 (* J (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
24×add-exp-log
18×add-cbrt-cube
15×pow-prod-down prod-exp cbrt-unprod
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
7×associate-*r*
6×cbrt-prod
4×sqrt-div add-log-exp
2×flip3-+ pow1/3 associate-*r/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 71
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
22.0ms
(* (* (* -2.0 (* J (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cbrt (cos (/ K 2.0)))
18.0ms
(cbrt (cos (/ K 2.0)))
36.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
47.0ms
(* (* (* -2.0 (* J (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify50.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
051701358

prune278.0ms

Filtered
54 candidates to 83 candidates (-53.7%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New80383
Fresh189
Picked011
Done011
Total811394

Merged error: 10.7b

Counts
94 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cbrt (cos (/ K 2.0))))
0.3b
(cbrt (cbrt (cos (/ K 2.0))))
7.1b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.6b
(* (* (* -2.0 (* J (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0)))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
73×pow1
72×add-exp-log
55×pow-prod-down prod-exp cbrt-unprod
50×add-cbrt-cube
18×cbrt-prod
15×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
8×sqrt-prod
7×associate-*r*
4×sqrt-div add-log-exp
2×flip3-+ pow1/3 associate-*r/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 101
Calls
4 calls:
2.0ms
(cbrt (cbrt (cos (/ K 2.0))))
2.0ms
(cbrt (cbrt (cos (/ K 2.0))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
34.0ms
(* (* (* -2.0 (* J (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0)))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series121.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(cbrt (cbrt (cos (/ K 2.0))))
18.0ms
(cbrt (cbrt (cos (/ K 2.0))))
34.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
49.0ms
(* (* (* -2.0 (* J (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0)))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify50.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050272072

prune329.0ms

Filtered
60 candidates to 113 candidates (-88.3%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1112113
Fresh01010
Picked101
Done022
Total11214126

Merged error: 10.7b

Counts
126 → 14

regimes757.0ms

Accuracy

92.1% (0.4b remaining)

Error of 13.5b against oracle of 13.0b and baseline of 18.7b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04599
14599

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.3s1495×body1280valid
724.0ms1258×body640valid
496.0ms4260×body80valid
272.0ms650×body320valid
90.0ms337×body160valid
0.0ms1×body80invalid

Profiling

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